Regardless of the LTC issue (I'd say it's likely "don't ask, don't tell" with regard to suitability), you'd likely have to lie on a 4473. The 4473 background check form very explicitly states that marijuana is federally illegal and it doesn't matter if your state has decriminalized it, you are prohibited from having guns.
So, if you do partake, you're committing perjury on a federal form anytime you buy a gun at a dealer and check the "No" box regarding drug use. Unless your purchase was just "holding it for a friend."
Do I agree with it? Hell no. But that's the way it is written.
But back to the LTC. I'd say it wouldn't be a stretch for an issuing officer to deny you an LTC if he knew you were either a user or a buyer. Again, as noted above, MJ use makes you a prohibited person. The question would be whether or not the issuing authority actually knew you bought or not (had access to shop records, for example). In that case, the less said the better.
This is also part of the reason GOAL had the campaign around, "If you like having gun rights, be careful of dispensaries and MA legal marijuana" - because it's a bit of a quagmire on the federal level.